Extendability and domains of holomorphy in infinite-dimensional spaces

Richard M. Aron, Stéphane Charpentier, Paul M. Gauthier, Manuel Maestre, Vassili Nestoridis Annales Polonici Mathematici MSC: Primary 46G20; Secondary 58B12. DOI: 10.4064/ap180821-5-12 Published online: 12 April 2019


We study the notions of extendability and domain of holomorphy in the infinite-dimensional case. In this setting it is also true that the notions of domain of holomorphy and weak domain of holomorphy are equivalent. We also prove that the set of non-extendable functions belonging to some classes $X(B)\subset H(B)$, $B$ being the open unit ball in a separable complex Banach space, is a lineable and dense $G_\delta .$ Moreover, when $\varOmega $ is $H_b$-holomorphically convex (defined in the text), it is shown that the set of non-extendable holomorphic functions on $\varOmega $ is a lineable and dense $G_\delta $ set.


  • Richard M. AronDepartment of Mathematical Sciences
    Kent State University,
    Kent, OH 44242, U.S.A.
  • Stéphane CharpentierCentre de Mathématiques
    et Informatique (CMI)
    Bureau 303
    Aix-Marseille Université
    Technopôle Château-Gombert
    39, rue F. Joliot Curie
    13453 Marseille Cedex 13, France
  • Paul M. GauthierDépartement de Mathématiques et de Statistique
    Université de Montréal
    Montréal, Que., H3C 3J7, Canada
  • Manuel MaestreDepartamento de Análisis Matemático
    Universidad de Valencia
    46100 Burjassot (Valencia), Spain
  • Vassili NestoridisDepartment of Mathematics
    University of Athens
    15784 Panepistemiopolis
    Athens, Greece

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